Perturbation Estimation Research Articles

A multivariable adaptive control method for aeroengine with H∞ performance considering engine output limitation protection based on fully adjustable Neural Network

Aeroengines, being highly nonlinear systems subject to external disturbances, present a challenge for conventional control methods in achieving satisfactory performance. The radial basis function neural networks possess the capability to effectively model highly approximate nonlinear functions, making them suitable for implementation in aeroengine control. However, the radial basis function (RBF) neural network is a local approximation model that inadequately incorporates historical information. Additionally, the tracking error of neural networks can also impact control effectiveness. To address this issue, this paper proposes a multivariable control method for aeroengines with H∞ performance based on fully adjustable Long Short-term Memory-Radial Basis Function Neural Network (LSTM-RBFNN). Firstly, a factual mathematical model of an aeroengine is established based on the principles of aerodynamics and thermodynamics. Secondly, the paper proposed an LSTM-RBF neural network architecture to enhance prediction performance and proposed using a finite time perturbation estimator to gauge the approximate error of neural networks, thereby acquiring immeasurable approximative error information. Then, in order to mitigate the influence of neural network tracking error on the loop, the estimated errors are incorporated into the primary loop controller, and a static state disturbance full feedback H∞ controller is proposed. Then, leveraging the LSTM-RBF architecture proposed in this study, we further employ Taylor expansion of nodes to derive the adaptive law of the neural network and propose a novel neural network adaptive law that incorporates tracking error estimated by the disturbance observer into the adjustment mechanism to enhance tracking performance. The stability of this adaptive law has been proven based on Lyapunov function analysis. And considering the output limitation protection problem of aeroengine, a virtual command value based limitation protection method is proposed for the above control method, and it is proved that this limitation method does not damage the stability and design process of the original control method. Finally, numerical simulation and hardware in loop simulation experiments were conducted, and the results showed that under the same adaptive gain of the neural network, the performance indicators (IAE, IATE, σ) could be reduced by more than 50% compared to other methods, which demonstrates superior tracking and disturbance rejection performance achieved by our proposed method.

Lipschitz regularity for Poisson equations involving measures supported on C 1,Dini interfaces

We prove optimal Lipschitz regularity of solutions to Poisson’s equation with measure data supported on a C 1 , Dini interface and with C 0 , Dini density. We achieve this by deriving pointwise gradient estimates on the interface, further showing the piecewise differentiability of solutions up to this surface. Our approach relies on perturbation arguments and estimates for the Green’s function of the Laplacian. Additionally, we provide sharp counterexamples highlighting the minimality of our assumptions.

Estimation of Dose Perturbation Due to the Presence of Metal Hip Prostheses in Radiotherapy with Electron and Photon Beams: A Monte Carlo Study

Purpose: The impact of various hip prosthesis materials on the amount of dose perturbation generated by 9 MeV electron and 18 MV photon beams during pelvic radiation therapy is analyzed in this research. Materials and Methods: The Varian 2100 C/D LINAC head for the electron (9 MeV) and photon (18 MV) modes and a water phantom with a realistic hip prosthesis were modeled using the Monte Carlo (MC) code; MCNPX (Ver. 2.6.0) and were benchmarked for measurement. Four different materials, including Cobalt–Chromium–Molybdenum-alloy (CCM), Stainless Steel (SS), Titanium, and Titanium-alloy (Ti-alloy) were evaluated. The changes in electron and photon fluences and dose perturbations due to the presence of the hip prostheses were investigated. Results: An increased dose of 13.29%, 13.77%, 6.16%, and 5.93% for 9 MeV and 30.43%, 33.05%, 10.89%, and 11.27% for 18 MV was calculated for Ti-alloy, Ti, CCM, and SS prosthesis, respectively. At 0.5 mm distance from the prosthesis, the Electron Backscatter Factor (EBF) of 1.31, 1.33, 1.15, and 1.14 for 9 MeV and 1.32, 1.34, 1.11, and 1.12 for 18 MV was calculated for Ti-alloy, Ti, CCM, and SS prosthesis, respectively. Dose perturbation is higher at a near distance from the prosthesis; by reducing the distance from the Ti-alloy prosthesis (1.5 to 0.5 mm), an increased dose of 7.70% and 5.54% resulted in 18 MV and 9 MeV, respectively. The dose decreases of up to 21% behind the hip prosthesis were calculated for 18 MV. Conclusion: It is essential to consider the dose perturbation due to the presence of a hip prosthesis to achieve the optimal treatment planning in radiotherapy.

Robust 3-D Path Following Control Framework for Magnetic Helical Millirobots Subject to Fluid Flow and Input Saturation.

Precise trajectory control is imperative to ensure the safety and efficacy of in vivo therapy employing the magnetic helical millirobots. However, achieving accurate 3-D path following of helical millirobots under fluid flow conditions remains challenging due to the presence of the lumped disturbances, encompassing complex fluid dynamics and input frequency saturation. This study proposes a robust 3-D path following control framework that combines a disturbance observer for perturbation estimation with an adaptive finite-time sliding mode controller for autonomous navigation along the reference trajectories. First, a magnetic helical millirobot's kinematic model based on the 3-D hand position approach is established. Subsequently, a robust smooth differentiator is implemented as an observer to estimate disturbances within a finite time. We then investigate an adaptive finite-time sliding mode controller incorporating an auxiliary system to mitigate the estimated disturbance and achieve precise 3-D path tracking while respecting the input constraints. The adaptive mechanism of this controller ensures fast convergence of the system while alleviating the chattering effects. Finally, we provide a rigorous theoretical analysis of the finite-time stability of the closed-loop system based on the Lyapunov functions. Utilizing a robotically-actuated magnetic manipulation system, experimental results demonstrate the efficacy of the proposed approach in terms of the control accuracy and convergence time.

Factorized Quadruples and a Predictor of Higher-Level Correlation in Thermochemistry.

Coupled cluster theory has had a momentous impact on the ab initio prediction of molecular properties, and remains a staple ingratiate in high-accuracy thermochemical model chemistries. However, these methods require inclusion of at least some connected quadruple excitations, which generally scale at best as with the number of basis functions. It is very difficult to predict, a priori, the effect correlation of past CCSD(T) on a given reaction energy. The purpose of this work is to examine cost-effective quadruple corrections based on the factorization theorem of the many-body perturbation theory that may address these challenges. We show that the factorized CCSD(TQf) method introduces minimal error to predicted correlation and reaction energies as compared to the CCSD(TQ). Further, we examine the performance of Goodson's continued fraction method in the estimation of CCSDT(Q)Λ contributions to reaction energies as well as a "new" method related to %TAE[(T)] that we refer to as a scaled perturbation estimator. We find that the scaled perturbation estimator based upon CCSD(TQf)/cc-pVDZ is capable of predicting CCSDT(Q)Λ/cc-pVDZ contributions to reaction energies with an average error of 0.07 kcal mol-1 and an L2D of 0.52 kcal mol-1 when applied to a test-suite of nearly 3000 reactions. This offers a means by which to reliably "ballpark" how important post-CCSD(T) contributions are to reaction energies while incurring no more than CCSD(T) formal cost and a little mental math.

Detecting adversarial samples by noise injection and denoising

Deep learning models are highly vulnerable to adversarial examples, leading to significant attention on techniques for detecting them. However, current methods primarily rely on detecting image features for identifying adversarial examples, often failing to address the diverse types and intensities of such examples. We propose a novel adversarial example detection method based on perturbation estimation and denoising to overcome this limitation. We develop an autoencoder to predict the latent adversarial perturbations of samples and select appropriately sized noise based on these predictions to cover the perturbations. Subsequently, we employ a non-blind denoising autoencoder to remove noise and residual perturbations effectively. This approach allows us to eliminate adversarial perturbations while preserving the original information, thus altering the prediction results of adversarial examples without affecting predictions on benign samples. Inconsistencies in predictions before and after processing by the model identify adversarial examples. Our experiments on datasets such as MNIST, CIFAR-10, and ImageNet demonstrate that our method surpasses other advanced detection methods in accuracy.

An efficient illumination compensation method for reverse time migration

AbstractBy directly solving the full two‐way wave equation, reverse time migration has superiority over other imaging algorithms in handling steeply dipping structures and other complicated geological models. Moreover, by incorporating the asymptotic inversion operator into reverse time migration imaging condition, the imaging algorithm is able to give a quantitative estimation of parameter perturbation in high‐frequency approximation sense. However, because conventional asymptotic inversion only accounts for geometrical spreading, uneven illumination due to irregular acquisition geometry and inhomogeneous subsurface at each image point is neglected. The omit of illumination compensation significantly affects the imaging quality. Wave‐equation‐based illumination compensation methods have been extensively studied in the past. However, the traditional wave‐equation‐based illumination compensation methods usually require high computational cost and huge storage. In this paper, we propose an efficient wave‐equation‐based illumination compensation method. Under high‐frequency approximation, we first define a Jacobian determinant to measure the regularity of subsurface illumination, and then illumination compensation operators are proposed based on the Jacobian. Through boundary integration, we further express the illumination compensation operators through extrapolated wavefields; the explicit computation of asymptotic Green's functions is thus avoided, and an efficient illumination compensation implementation for reverse time migration is achieved. Numerical results with both synthetic and field data validate the effectiveness and efficiency of the presented method.

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory.

Coupled cluster methods based exclusively on double excitations are comparatively "cheap" and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

Heavy quark dynamics via the Gribov-Zwanziger approach

In this work, we investigate the momentum-dependent drag and diffusion coefficient of heavy quarks (HQs) moving in the quark-gluon plasma background. The leading order scattering amplitudes required for this purpose have been obtained using the Gribov-Zwanziger propagator for the mediator gluons to incorporate the nonperturbative effects relevant to the phenomenologically accessible temperature regime. The drag and diffusion coefficients so obtained have been implemented to estimate the temperature and momentum dependence of the energy loss of the HQ as well as the temperature dependence of the specific shear viscosity (η/s) of the background medium. Our results suggest a higher energy loss of the propagating HQ compared to the perturbative estimates, whereas the η/s is observed to comply with the AdS/CFT estimation over a significantly wider temperature range compared to the perturbative expectation. Published by the American Physical Society 2024

Perturbation estimation based single-loop decoupling control strategy for DC-based DFIG to augment MPPT and FRT capabilities

This paper proposes a single-loop decoupling controller with high-gain perturbation observer (HP-FLC) for double-VSC DFIG which can be connected to DC grid to extract maximum wind power and improve fault ride-through (FRT) capability. Lumped perturbation terms are defined in the HP-FLC to include all unknown, time-varying dynamic and external perturbations, which are actively estimated by high-gain perturbation observer. Then, a more time-efficient single-loop feedback decoupling controller is designed to compensate the perturbation estimation. This control strategy combines the advantages of classical feedback controller and perturbation observer, which is separated from the accurate system model and easy to implement. Simulation results show that the proposed control strategy can achieve better wind power extraction and stronger FRT capability compared with double-loop feedback linearization controller (DL-FLC) and single-loop feedback linearization controller (SL-FLC), and the transient performance is better than that of the sliding-mode feedback controller (SMC-FLC). Finally, an experimental platform is built to confirm the practical implementation of the proposed approach.

Влияние скорости вращения и фигуры астероида на величину возмущений в его вращательной динамике при тесном сближении с Землей

By means of numerical experiments, the influence of the value of the asteroid’s own rotational velocity, orientation of the axis of rotation, and figure parameters on the magnitude of perturbations in its rotational dynamics arising during close approach to the Earth is studied. Two cases are considered: 1) asteroid (99942) Apophis with a relatively slow rotation (period ≈ 30 h) and 2) asteroid 2012 TC4, which has a fast rotation (period ≈ 12 min). It was found that in the case of asteroids with slow rotation, perturbations can be large: in the case of Apophis, when approaching the Earth in 2029, changes in the rotational period ∆P may reach tens of hours, and deviations in the orientation of the axis of rotation ∆γ — tens of degrees. For fast-rotating asteroids, the perturbations are very small: in the case of asteroid 2012 TC4 at its approach to the Earth in 2017, |∆P | < 10−5 min, |∆γ| < 0.01◦. It is shown that for asteroids with slow rotation, the uncertainty in the determination of asteroid figure parameters (moments of inertia) can lead to noticeable inaccuracies in the estimation of perturbation magnitudes. The uncertainty in the knowledge of the figure parameters of a fast-rotating asteroid practically does not affect the estimation of perturbations in its rotational dynamics. In the case of Apophis, changes in the rotational velocity and orientation of the axis of rotation during the upcoming 2029 approach to the Earth may lead to a decrease in the value of the parameter A2, which characterizes the Yarkovsky effect, to −1.5 · 10−14 a.u./d2, or to an increase up to −3.5 · 10−14 a.u./d2. Perturbations in the rotational dynamics of asteroid 2012 TC4 during its approach to the Earth in 2017 did not affect the value of parameter A2.

Impacts of inter-satellite links on the ECOM model performance for BDS-3 MEO satellites

Inter-satellite link (ISL) plays an essential role in current and future Global Navigation Satellite System (GNSS). In this study, we investigate the impact of ISL observations on precise orbit determination for BeiDou-3 Navigation Satellite System (BDS-3) Medium Earth Orbit (MEO) satellites based on different Extended CODE Orbit Models (ECOM). Thanks to the better observation geometry of the Ka-band ISL data compared to the L-band data for BDS-3 MEO satellites, the ISL solution substantially reduces Orbit Boundary Discontinuity (OBD) errors, except for C30, which suffers from unstable Ka-band hardware delay. From the external quality analysis, ISL significantly enhances the reliability of the orbit of MEO satellites manufactured by the China Academy of Space Technology (CAST). The standard deviation (STD) of the satellite laser ranging (SLR) residuals is approximately 2.5 cm, and the root mean square (RMS) is reduced by 10–23% compared to L-band solutions. Besides, the Sun-elongation angle dependent systematic error in SLR residuals nearly vanishes based on the reduced 5-parameter ECOM (ECOM1) or extended 7-parameter ECOM (ECOM2) with ISL data. This is because the ISL reduces the correlation between state parameters and solar radiation pressure (SRP) parameters as well as those among SRP parameters, leading to a more accurate estimation of both orbit and SRP perturbations, particularly those along B direction. This confirms that the deficiency of the SRP models for BDS-3 CAST satellites can be compensated by using better observation geometry from ISL data. On the other hand, for the satellite manufactured by Shanghai Engineering Center for Microsatellites (SECM), the ISL allows for a more accurate estimation of the Bc1 parameter in the ECOM1 model. This only reduces linear systematic error, possibly because the impact generated by the satellite bus cannot be entirely absorbed by the B-direction parameters.

A linearly implicit finite element full-discretization scheme for SPDEs with nonglobally Lipschitz coefficients

Abstract The present article deals with strong approximations of additive noise driven stochastic partial differential equations (SPDEs) with nonglobally Lipschitz nonlinearity in a bounded domain $ \mathcal{D} \in{\mathbb{R}}^{d}$, $ d \leq 3$. As the first contribution, we establish the well-posedness and regularity of the considered SPDEs in space dimension $d \le 3$, under more relaxed assumptions on the stochastic convolution. This improves relevant results in the literature and covers both the space-time white noise ($d=1$) and the trace-class noises ($\text{Tr} (Q) < \infty $) in multiple dimensions $d=2,3$. Such an improvement is achieved based on a key perturbation estimate for a perturbed PDE, with the aid of which we prove the convergence and uniform regularity of a spectral approximation of the SPDEs and thus get the improved regularity results. The second contribution of the paper is to propose and analyze a spatio-temporal discretization of the SPDEs, by incorporating a standard finite element method in space and a linearly implicit nonlinearity-tamed Euler method for the temporal discretization. The proposed time-stepping scheme is linearly implicit and does not suffer from solving nonlinear algebra equations as the backward Euler scheme does. Based on the improved regularity results, we recover the expected strong convergence rates of the fully discrete scheme and reveal how the convergence rates rely on the regularity of the noise process. In particular, a classical convergence rate of order $O(h^{2} +\tau )$ can be obtained even in high dimension $d=3$, as the driven noise is of trace class and satisfies certain regularity assumptions. The optimal error estimates turn out to be challenging and face some essential difficulties when the tamed time-stepping scheme meets the finite element spatial discretization, particularly in the context of low regularity and multiple dimensions $d \le 3$. Some highly nontrivial arguments are introduced to overcome the difficulties. Finally, numerical examples corroborate the claimed strong orders of convergence.

Saturated Sliding Mode Control Scheme for a New Wearable Back-Support Exoskeleton

Low back pain has been torturing people around the world as a common and chronic disease, the main inducement of which is lumbar disc herniation (LDH). To alleviate patients’ pain noninvasively, this paper proposes a new lumbar spinal rehabilitation exoskeleton. This exoskeleton is composed of two bands connected by four motor-driven piston pushrods, where the range of band can be adjusted to adapt to people with different waistlines. The four pushrods provide support forces to hold the upper body to relieve the burden of lumbar. The joints between pushrods and band are universal pairs and spherical pairs. The whole structure can be regarded as a parallel robot, thus the supporting and waist tracking performance can be determined by motion control effect of pushrods. Considering the motor torque of pushrods is limited, in this paper, a saturated sliding mode control scheme is proposed. Meanwhile, an extended state observer (ESO) is employed to estimate the external disturbance and internal uncertainties, then the estimates of perturbations will be compensated by the feedback scheme. Furthermore, to enhance the disturbance-tracking performance of the ESO an integrated sliding mode observer is proposed to compensate the tracking errors of ESO. The stabilities of controller and observers are proved by Lyapunov stability theory. Finally, a simulation and two experiments are conducted to verify the performance of the proposed controller and the new exoskeleton. The simulation results show that the novel/new controller can drive the new exoskeleton to move along with the desirable trajectory to support the upper body so that alleviating the burden of waist. The results of myoelectricity experiments also show favorable effectiveness of exoskeleton on supporting upper body in different postures. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —this article was inspired by the concerns of low back pain that many people are suffering. Most existing rehabilitation robots tend to focus on supporting lower body and arms, while back-support rehabilitation robots are barely seen. Although we can see a few upper-body supporting robots in sporadic papers, these studies have not proposed a good control scheme yet. Besides, it is difficult to find a rehabilitation robot with simple structure as well as conforming to ergonomics. To resolve the shortcomings of the structure of existing robots and control models, we proposed a completely new rehabilitation robot with novel mechanical structure. Meanwhile, a new saturated sliding mode and novel integrated observer are employed in the position-force control system to enhance the stability and controllability of the whole robot control system. Then, some elaborately designed experiments are conducted to test the proposed robot and the control system. Numerical results demonstrate that the proposed method can significantly increase the trajectory tracking performance and alleviate low back pain.

Observer-based differential evolution constrained control for safe reference tracking in robots

Big torque inputs in controls could increase energy consumption, and big estimated perturbations in observers could produce device damages. Therefore, it would be interesting to propose a constrained control for safe reference tracking and a constrained observer for safe perturbation estimation in robots. Furthermore, the best gains in controls produce a balance between safe reference tracking and save energy consumption. Therefore, it would be interesting to propose a method to find the best gains. In this paper, an observer-based differential evolution constrained control is proposed for safe reference tracking in robots. The contributions are described as follows: (1) a constrained observer is proposed for safe perturbation estimation in robots, (2) a constrained control is proposed for safe reference tracking in robots, (3) a differential evolution optimizer is used to find the best gains in an observer-based constrained control, (4) the robust stability in an observer-based constrained control is assured, (5) the pseudo-code of an observer-based differential evolution constrained control is detailed. The proposed observer-based differential evolution constrained control is applied for safe reference tracking in two robots.

Robustness and Eventual Slow Decay of Bound States of Interacting Microwave Photons in the Google Quantum AI Experiment

Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multimagnon bound states in the celebrated XXZ spin-chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan , Nature , 240 (2022)] realizing the Floquet model has demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic nonintegrable systems. Here, we study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes. Published by the American Physical Society 2024

Predefined time backstepping control of photovoltaic grid connected inverter

The large-scale grid connection of photovoltaic (PV) systems creates great hazards to the operation of power equipment and has a great impact on the stability and reliability of power systems. To achieve stable control and flexible management of PV grid connection, a predefined time adaptive backstepping control method based on the predefined boundary is proposed. Based on the predefined boundary time-varying function, the user’s predefined boundary design of the control signal is accomplished to ensure the boundedness of the global signal, which is independent of the initial state of the system. The controller with predefined boundaries is designed based on backstepping control, and the estimation and compensation of perturbations are attained based on adaptive control. The global predefined time stability of the predefined boundary of the closed-loop system is certified using the Lyapunov function. Simulation studies attest to the performance of the predefined time control strategy.

Robust Current Control for Grid-Connected VSC: Nonlinear Adaptive Control with Perturbation Estimation

This paper introduces a robust control strategy for grid-connected voltage source converters using Nonlinear Adaptive Control (NAC) enhanced by a perturbation observer (PO). This approach precisely regulates grid current and adapts to unknown dynamics, time-varying parameters, and disturbances impacting the system. By estimating and compensating for these perturbations, the strategy achieves adaptive feedback linearization, effectively managing the system’s inherent nonlinearity without requiring an exact model or extensive measurements. The NAC offers substantial improvements over traditional vector control and feedback linearization, particularly under conditions where grid voltage significantly deviates from normal levels. Simulation results confirm the superior performance of the proposed method.

Global classical solution of the Cauchy problem to the 3D Benjamin–Bona–Mahony–Burgers-type equation with nonlocal control constraints

Abstract This article focuses on the Cauchy problem of the Benjamin–Bona–Mahony–Burgers (BBMB) equation with nonlocal control constraints in ℝ 3 {\mathbb{R}^{3}} . We employ the Phragmén–Lindelöf decomposition method and Green’s function to investigate global classical solutions and their long-term behaviors, including optimal estimates for finite density initial perturbation. Additionally, optimal solutions near the minimal mass ground state are analyzed.

Robust proportional control for trajectory tracking using parameter and perturbation adaptive estimators

The principal contribution of this paper is the feedback design of an output trajectory tracking controller applied to a certain class of mechanical systems. The controller does not need velocity measurements for its implementation and achieves the trajectory tracking control aim. We propose adaptive estimators to determine the plant parameters and constant external perturbations. When the plant is affected by time-variant external perturbations, an observer filter that can be implemented to recover an estimation of the time-variant perturbations can replace the adaptive estimator. The closed-loop stability is analysed throughout Lyapunov tools. We illustrate the performance of the proposed control structure via numerical simulations and experiments, the numerical simulations are carried out for a pendulum coupled to a DC motor and the experiments are accomplished for a mass-spring-damper system.